On using bi-equational constraints in CAD construction

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Volumn 2005, Issue , 2005, Pages 76-83

  Brown, Christopher W ^a   McCallum, Scott ^b  

^a UNITED STATES NAVAL ACADEMY   (United States)

^b MACQUARIE UNIVERSITY   (Australia)

Author keywords

CAD; Polynomial systems

Indexed keywords

ALGEBRA; POLYNOMIALS;

CYLINDRICAL ALGEBRAIC DECOMPOSITIONS (CAD); POLYNOMIAL EQUATIONS; POLYNOMIAL SYSTEMS; QUANTIFIER ELIMINATION PROBLEMS;

CONSTRAINT THEORY;

EID: 33749575816     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1073884.1073897     Document Type: Conference Paper

References (19)

1. S. S. Abhyankar. Algebraic Geometry for Scientists and Engineers. American Math. Society, 1990.
2. D. S. Arnon. Topologically reliable display of algebraic curves. In Proceedings of SIGGRAPH, pages 219-227, 1983.
3. D. S. Arnon, G. E. Collins, and S. McCallum. Cylindrical algebraic decomposition I: The basic algorithm. SIAM Journal on Computing, 13(4):865-877, 1984.
4. James C. Beaumont, Russell J. Bradford, James H. Davenport, and Nalina Phisanbut. A poly-algorithmic approach to simplifying elementary functions. In Proc. International Symposium on Symbolic and Algebraic Computation, pages 27-34, 2004.
5. C. W. Brown. Improved projection for cylindrical algebraic decomposition. Journal of Symbolic Computation, 32(5):447-465, November 2001.
6. C. W. Brown. Simple CAD construction and its applications. Journal of Symbolic Computation, 31(5):521-547, May 2001.
7. Christopher W. Brown. QEPCAD B: a program for computing with semi-algebraic sets using CADs. ACM SIGSAM Bulletin, 37(4):97-108, 2003.
8. B.F. Caviness and J. R. Johnson, editors. Quantifier Elimination and Cylindrical Algebraic Decomposition. Texts and Monographs in Symbolic Computation. Springer-Verlag, 1998.
9. G. B. Collins. Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition. In Lecture Notes In Computer Science, volume Vol. 33, pages 134-183. Springer-Verlag, Berlin, 1975, Reprinted in [8].
10. G. E. Collins. Quantifier elimination by cylindrical algebraic decomposition - 20 years of progress. In B. Caviness and J. Johnson, editors, Quantifier Elimination and Cylindrical Algebraic Decomposition, Texts and Monographs in Symbolic Computation. Springer-Verlag, 1998.
11. G. E. Collins and H. Hong. Partial cylindrical algebraic decomposition for quantifier elimination. Journal of Symbolic Computation, 12(3):299-328, Sep 1991.
12. H. Hong. Quantifier elimination for formulas constrained by quadratic equations via slope resultants. Computer J., 36(5):440-449, 1993.
13. M. Morden. Geometry of Polynomials, 2nd edition. American Math. Society, 1966.
14. S. McCallum. An improved projection operation for cylindrical algebraic decomposition of three-dimensional space. Journal of Symbolic Computation, 5(1,2):141-161, 1988.
15. S. McCallum. An improved projection operator for cylindrical algebraic decomposition. In B. Caviness and J. Johnson, editors, Quantifier Elimination and Cylindrical Algebraic Decomposition, Texts and Monographs in Symbolic Computation. Springer-Verlag, Vienna, 1998.
16. S. McCallum. Factors of iterated resultants and discriminants. Journal of Symbolic Computation, 27:367-385, 1999.
17. S. McCallum. On projection in CAD-based quantifier elimination with equationsl constraint. In Sam Dooley, editor, Proc. International Symposium on Symbolic and Algebraic Computation, pages 145-149, 1999.
18. S. McCallum. On propagation of equationsl constraints in CAD-based quantifier elimination. In Bernard Mourrain, editor, Proc. International Symposium on Symbolic and Algebraic Computation, pages 223-230, 2001.
19. H. Whitney. Complex Analytic Varieties. Addison-Wesley, 1972.